Details

sample93.0ms

Algorithm

intervals

Results

52.0ms	119×	body	1280	valid
16.0ms	19×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 39.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series137.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune131.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	38	9	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	9	48

Merged error: 14.0b

Counts

48 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
16.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series750.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	559	2923
1	2054	2373
2	5001	2349

prune377.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	170	11	181
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	176	14	190

Merged error: 13.8b

Counts

190 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.7b	(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`tan-quot`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 79

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
1.0ms	(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (tan x)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
477.0ms	(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (tan x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	199	781
1	625	688
2	2402	687
3	5001	683

prune317.0ms

Filtered

91 candidates to 72 candidates (79.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	87	18	105

Merged error: 13.8b

Counts

105 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin eps) (cos eps))
0.2b	(* (tan x) (tan eps))
5.0b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
103×	`times-frac`
86×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
63×	`prod-diff`
24×	`distribute-lft-out`
21×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`pow1` `associate-/r` `div-inv` `associate-/l` `add-log-exp`
5×	`tan-quot` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`frac-times` `sub-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 185

Calls

4 calls:

4.0ms	(/ (sin x) (cos x))
4.0ms	(/ (sin eps) (cos eps))
5.0ms	(* (tan x) (tan eps))
28.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

series493.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (sin x) (cos x))
17.0ms	(/ (sin eps) (cos eps))
87.0ms	(* (tan x) (tan eps))
366.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify73.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	656	3455
1	2255	2808
2	5001	2771

prune501.0ms

Filtered

197 candidates to 118 candidates (59.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	198	17	215

Merged error: 12.4b

Counts

215 → 17

regimes191.0ms

Accuracy

93.8% (0.6b remaining)

Error of 13.8b against oracle of 13.2b and baseline of 22.2b

bsearch120.0ms

Steps

Iters	Range		Point
9	5.825543930254655e-57	3.2910297204248635e-51	3.2412061887490125e-51
9	-6.669138218872808e-16	-2.3250751478766463e-21	-1.3356538430022876e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	46
1	37	46

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3281×	body	1280	valid
550.0ms	631×	body	2560	valid
391.0ms	1888×	body	640	valid
106.0ms	785×	body	320	valid
45.0ms	1088×	body	80	valid
30.0ms	327×	body	160	valid